# Wiener model

The **Wiener model** (after the American mathematician Norbert Wiener ) is a special type of model for nonlinear dynamic systems . The characteristic is the structure, consisting of the series connection of a linear time-invariant dynamic system and a static non-linearity. In the Hammerstein model , the same elements are arranged in a different order.

The Wiener model is defined for both single-variable and multi-variable systems .

The Wiener model is generally used in control engineering, for example in modeling , system identification and controller design.

For single-variable systems, the mathematical description is

- ,

in which

- is the impulse response belonging to the transfer function of the linear system and
- denotes the convolution operator .